In-process relative robot workcell calibration

ABSTRACT

A relative calibration system and method for robot workcell calibration is capable of correcting errors between the robot tool center point (TCP) and the work-object frame according to a relative reference, in that a precision path will be created based on this calibrated workcell.

FIELD OF THE INVENTION

[0001] This invention relates generally to a system and method forcalibrating a virtual robot tool center point (TCP) or virtualwork-object frame and more particularly to the use of relativemeasurement to perform in-process workcell calibration.

BACKGROUND OF THE INVENTION

[0002] Industry is now seeing a dramatic increase in robot simulationand off-line programming. In order to use off-line programmingeffectively, the simulated workcell has to be identical to the realworkcell. This requires a more efficient and accurate method for robotcalibration. By making use of calibration, the simulated robot workcellwill clone the real workcell in a simulation model, so that the off-linegenerated robot program from a simulated workcell will be accurateenough and can be directly downloaded to a real robot controller todrive the real robot with maximum accuracy and without furthermodification.

[0003] A variety of attempts to develop a better robot calibrationsystem and method to improve robot accuracy exist in the prior art.Currently used techniques, however, are typically tedious, timeconsuming and expensive. This is because most of the prior artcalibration methodology so far is based on absolute calibration.

[0004] “Absolute calibration” refers to the method by which an externalcoordinate measurement system is utilized to measure the absoluteposition, often referred to as a global coordinate system. Since theexternal system measures the coordinates of a point in the workspace,the absolute method can validate any path accuracy. However, absoluteposition measurement has many drawbacks including the fact that it istime consuming, expensive and sometimes fails to meet accuracyrequirements. One example in the prior art is to use an opticalcoordinate measurement system (OCMS) to calibrate the robotic workcell,which is a very expensive and time-consuming way of calibrating therobot.

[0005] In contrast to absolute calibration, some development has beenmade in the area of “relative calibration”. Relative calibration is amethod in which a standard reference target is used as the precisionreference for the correction of robot kinematic error. This “standardreference” provides high-precision relative geometric quantities such aslength, circularity and linearity. A standard reference could simply bea bar, a cube, a cylinder, or a ball. During the calibration, the robotis driven to make the tool center point (TCP) follow the geometry of theselected standard reference. This standard reference therefore providesa constraint on the TCP process. Due to the kinematic error, thisconstraint would be violated if the nominal kinematic model were used tocalculate the Cartesian coordinates from the same joint angles.Minimization of the constraint violation (constraint error) will givethe values of error parameters. In the present invention, this standardis called “relative reference.”

[0006] However, all known relative calibration techniques are only forone component calibration. There is no relative calibration technique todeal with the overall workcell calibration. Accordingly there is a needfor an economical calibration method and apparatus to deal with overallworkcell calibration.

[0007] Moreover, the tool center point (TCP) may change due to tool wearor tool changes. The workpiece itself can introduce a significant amountof error or uncertainty due to workpiece variation or deflection duringthe manufacturing process. Real time calibration for each workpiece caneliminate this effect. Accordingly, there is a need to develop a methodand apparatus, which must be cost effective and capable of in-processoperation and real-time implementation.

SUMMARY OF THE INVENTION

[0008] In order to overcome the shortcomings and drawbacks ofconventional calibration systems and methods to make calibrationcost-effective, efficient and easy to use, the objective of the presentinvention is to create a novel method and device for robotic workcellcalibration. The present invention will provide an economical, robustcalibration system that will have the ability to calibrate the majorconsiderations involved in any robot system including calibration on areal-time basis during manufacturing processes.

[0009] Generally speaking, there are two types of setups in roboticworkcells. One consists of the robot holding the tool and workpiecebeing fixed on the worktable. This is called “Moving TCP”. The othertype consists of the robot holding the workpiece and the tool is fixedon the floor. This is called “Fixed TCP”.

[0010] In a fixed TCP-based robotic workcell, the forward kinematicchain includes the robot (robot based coordinate), the gripper(work-object coordinate) and the workpiece (object coordinate); thebackward kinematic chain includes the tooling system (tool coordinate).In an ideal case, the errors of real or virtual contact points betweenthe tooling and the object are zeros along the working path.

[0011] All of the errors from the two kinematic chains can be divided intwo parts: “forward chain error” and “backward chain error”. Forwardchain error includes the robot error, the gripper-setup error, and theobject-installation error. Backward chain error includes tool-tableerror and tooling fixture error. The role of calibration is to eliminateor correct all of these errors in order to create highly accurate pathsfor robot operation. The same principle applies to a moving TCP-basedrobotic workcell.

[0012] In a conventional absolute calibration environment, the goal isto calibrate all the components related to a global absolute reference,in order to eliminate all of these errors separately. Absolute workcellcalibration includes robot TCP calibration, tooling calibration andwork-object coordinate calibration, wherein each is performedindividually. Each calibration process will measure all the Cartesiancoordinates to determine the error between the nominal and true value.

[0013] Unlike conventional absolute calibration methods, the relativecalibration method of the present invention treats all of the errors asrelative error between the tooling and the working object compared to arelative reference. Measuring this relative error and finding a way tocorrect this error is a major advantage of this invention. As long asthe relative error is eliminated compared to the relative reference, theworkcell is calibrated related to the relative reference and the perfectpath will be generated.

[0014] Prior to beginning the relative calibration, a computer aideddesign (CAD) model of the workpiece is downloaded into a data collectionand computing device such as a programmable controller or computer.

[0015] There are five steps for completing the relative calibration.

[0016] The first step is tool center point (TCP) calibration. Thisconsists of performing a TCP calibration using the robot as ameasurement tool. The calibration is accomplished by mounting acalibration target within the workcell and in a position that the robotcan reach from various orientations. The calibration target can be asphere, cylinder, cubic or any other definable geometric shape. Therobot is programmed to touch the calibration target surface from variousangles with a CMM touch probe. All contact positions are recorded. TheTCP is calculated from the measurements using a non-linear least squaresoptimization algorithm.

[0017] The second step is to set up a relative reference between therobot and a sample-working object. The relative reference is establishedby having the robot hold a finished sample of the working object(workpiece) while a series of measurements is performed to compensatefor the error between the perfect CAD model and the finished sample toobtain a relative reference. When the actual implementation of therelative method is considered, the enforcement of TCP to follow thestandard geometry becomes the biggest concern since the achievableaccuracy of a “standard reference” can be very high with moderatemanufacturing cost. This compensation process will make the standardreference in a cost-effective way. The actual TCP path becomes theequivalent reference when the enforcement error is treated as thereference geometric error. As a result, the relative reference is theperfect CAD model of the workpiece superposed by all of the systemerrors from the robot.

[0018] In the third step, the robot will hold a raw or unfinishedworkpiece and the measurement of the raw workpiece will generate arelative error map compared with relative reference set up in the secondstep.

[0019] In the fourth step, an error compensation matrix to calibrate thework-object coordinate, called virtual work-object coordinate, will becalculated based on the relative error map obtained in the third step.An iterative nonlinear optimization algorithm is employed to obtain thiserror compensation matrix.

[0020] In the last step, tooling system calibration will be performed.In the previous steps, the tooling system has not been involved becausethe calibration station simulates the role of the tooling system. Afterfinishing the calibration of the virtual work-object coordinate in thecalibration station, the robot is moved to touch the tooling system andobtain the residual error between the tooling system and the calibrationsensor in the calibration station. Compensation of this error into thefixed TCP will complete the tooling system calibration so that theoverall workcell calibration process will be completed.

[0021] These five steps complete the workcell calibration offline. Thesubsequent online calibration requires only two steps from those fivesteps. The first is taking relative measurements of a workpieceutilizing the robot and calibration station. The second step iscalculating a new, updated error compensation matrix for the virtualwork-object coordinate. These two steps can be performed in real-timeand in process.

[0022] It will be observed that the fundamental difference between theprior-art absolute calibration processes and the present invention isthat the present invention separates the manipulator error andnon-manipulator errors by utilizing a relative reference and relativecompensation matrix. All of the manipulator errors are assigned to arelative reference while the rest of the non-manipulator errors aredealt with by the virtual work-object coordinate in this process.

[0023] It is an object of this invention is to develop a relativecalibration method and apparatus to perform in-process calibration onthe working factory floor.

[0024] It is an object of this invention to provide a method to separatethe manipulator error from the non-manipulator installation errors. Inthis way, a straightforward linear calibration can be implemented inprocess.

[0025] It is an object of this invention to provide a relative referencefor relative error measurement. By using this relative reference, acost-effective high precision measurement tool can be easily utilized.

[0026] It is another object of the invention to provide a relativemeasurement system to measure relative error.

[0027] It is another object of this invention to provide an algorithm tocalculate the parameters of a virtual work-object coordinate matrix.

[0028] Finally, it is an object of the invention to provide a means forin-process implementation of the relative calibration.

[0029] In order to implement this method, the corresponding relativecalibration system must be integrated in the robotic workcell. Therelative calibration system used in this invention includes a roboticworkcell including a robot having an end effector. The end effectorfurther includes a gripper for gripping the workpiece. A new substationis added to the conventional robotic workcell, called a calibrationstation. A sensor for measuring the relative error between a workpieceand the relative reference is located in the calibration station. Withinthe calibration station there is also at least one calibration sample orcalibration target. In addition, a finished workpiece known to be withinallowable tolerance requirements is located within the station. A datacollection device for recording the output of the sensor and performingcalculations is also integrated into the workcell.

[0030] The sensor can be a non-contact or contact type lineardisplacement gauge. A preferred sensor used in the system is anon-contact optical displacement tool. The sensor consists of a diodelaser pointer and a linear charge couple device (CCD).

[0031] A contact mechanical measurement device could be a linearvariable differential transformer (LVDT). The LVDT is basically a seriesof inductors in a hollow cylindrical shaft and a solid cylindrical core.The LVDT produces an electrical output proportional to the position ofthe core.

DESCRIPTION OF THE DRAWINGS

[0032]FIG. 1 is a perspective view of a robotic grinding workcell andworkpiece calibration device;

[0033]FIG. 2 is a schematic view of the robot, gripper, workpiece and alinear displacement sensor;

[0034]FIG. 3 is a schematic view of the robot, gripper, workpiece and anon-contacting linear CCD sensor;

[0035]FIG. 4 is a flowchart showing the procedure of relative workcellcalibration.

[0036]FIG. 5 is a perspective view of a CMM touch probe and calibrationtarget;

[0037]FIG. 6 is a diagrammatic view of a probe and calibration target;

[0038]FIG. 7 is a graphical representation of a two-dimensional profileof an actual workpiece (in this instance a blade) and its computer aideddesign (CAD) model;

[0039]FIG. 8 is a graphical representation of the virtual work-objecterror model;

[0040]FIG. 9 is a flow chart showing two-stage optimization;

[0041]FIG. 10 depicts the measured relative error between a sampleworkpiece (again in this instance a blade) and an actual workpiece; and

[0042]FIG. 11 is a flow chart showing tool calibration.

DETAILED DESCRIPTION

[0043] Although the disclosure hereof is detailed and exact to enablethose skilled in the art to practice the invention, the physicalembodiments herein disclosed merely exemplify the invention that may beembodied in other specific structure. While the preferred embodiment hasbeen described, the details may be changed without departing from theinvention, which is defined by the claims. In this section, the bladegrinding is chosen as an example to describe the detail of methods andapparatus of this invention.

[0044]FIG. 1 shows an exemplary mechanical setup for a robotic grindingworkcell and work-object coordinate calibration device, generallyreferred to at reference numeral 10. The overall workcell is composed ofa robot 12, which is represented as a robot base coordinate systemoptionally a force sensor 20, for sensing three directional forces andtorques may be mounted on the robot mounting plate 14. The workcellfurther includes a gripper 30 mounted on the mounting plate or forcesensor that holds a workpiece 32. Also included is a tooling system 40such as a belt grinder 42 in which the belt 44 is supported by a contactwheel 46. Also within the workcell is a calibration station 50, in whichincludes a DB-G high accuracy and high resolution with 25 mm travelingrange linear gauge 52. The contact linear displacement sensor 52, robotarm, gripper 30 and workpiece 32 are shown in FIG. 2. Preferably and asshown in FIG. 3, a non-contact sensor or gage 54, such as a laser diodepointer and a linear charge coupled device (CCD) can be utilized.Non-contact sensors of this type are known in the art and generallyfunction by directing a laser beam of light toward the workpiece. Thelight beam is reflected and into a lens of on the sensor which thencalculates the distance from the sensor to the workpiece 32 or otherobject. Mounting the contact or non-contact linear gauge 52/54 close tothe work zone will increase the calibration accuracy. The workcell alsoincludes a computer 60, which stores a computer aid design (CAD) modelof the selected workpiece, generates the robot program by off-line robotprogramming software and downloads the program into the robot controller70. As will be discussed below, the workcell further includes acalibration target 80, such as a sphere.

[0045] An overview of the relative workcell calibration is shown in theflow chart of FIG. 4.

[0046] The first step of the calibration process is tool center point(TCP) calibration. As shown in FIGS. 5 and 6, a calibration target 80 ismounted within the robotic workcell in a position that the robot 12 canreach from various angles. Calibration target 80 can be any geometricshape such as a sphere, cylinder, cubic, etc. A CMM touch probe 34 isplaced in the robot gripper 30 or mounted to the end plate. The probe 34makes multiple contacts with the calibration target 80 as shown in FIG.6.

[0047] TCP calibration can be modeled as an optimization problem. Givena set of measurement data (robot position) and some constraints(geometry constraints), unknown parameters can be determined (robotcenter point on the mounting plate or gripper).

[0048] As shown in FIG. 6, given Yi and constraint f(Yi,a)=0, we mustfind a.

[0049] Yi=(xi, yi, zi) fits into the geometry model (for examplesphere).

[0050] Constraint f(Yi,a) is built based on the calibration approachthat depends on accuracy, cost, and calibration requirement.

[0051] Using a sphere model as the calibration reference target:

(xi−xo)²+(yi−y0)²+(zi−z0)² =R ²  (1)

[0052] Where R is known as the radius of the sphere and (xo, yo, zo) areunknown.

[0053] Each time contact is made, the measurements of robot position arerecorded. At the end of the calibration cycle, the TCP of the touchprobe is calculated.

[0054] There are numerous advantages of this method and apparatus fordetermining TCP. The traditional method of determining TCP consists ofmounting a pointer to a fixed position within the robotic workcell and asecond pointer to the robot end plate or gripper. The two pointers arethen aligned to determine the TCP. Because it is necessary to achieve“point to point” alignment, the robot must be moved manually to alignthe pointers. This is a very slow process. Secondly, the operator mustrely upon a visual inspection of the final pointer positions to insurethat the TCP has been determined. The necessity of operator visualconfirmation introduces potential error. The present method can beperformed by simply programming the robot to touch the geometric shapeat various or random points. Furthermore, there is no operator judgmentrequired that could introduce error into the TCP determination.

[0055] The next step is the relative reference setup. In an idealenvironment, the CAD model of the working object is a perfect relativereference. However, in the real case, and as shown for an exemplaryblade profile in FIG. 7, when the robot path goes through all targetpoints along the workpiece surface and the calibration station sensormakes a measurement at target point, the relative error will not bezero. That means:

f(i)=rb(i)+rg(i)+gw(i)  (2)

[0056] Where rb(i) is manipulator error, rg(i) is gripper installationerror and gw(i) is workpiece installation error.

[0057] The errors in equation 2 are regrouped into two separate groups.One is systematic error, which is a natural error from the robot 12. Italso is a nonlinear error. The other group is the installation errorsfrom the gripper and working-object. The installation errors can beadded into one resulting error.

[0058] In this way, the relative error can be rewritten as:

ref(i)=Δrobot(i)+Δwork-object frame(i)+ε  (3)

[0059] Where Δrobot(i) is the non-linear error mainly from robotmanipulator and Δwork-object frame(i) is the sum of the installationerrors from all of the rest of the components. This error can betransferred into the work-object coordinate, called the virtualwork-object matrix. It can be seen that the in-process workcellcalibration can be divided into two straightforward steps: the relativereference set up and the relative error calibration.

[0060] In this sense, the relative reference will be:

Relative Reference=f(x,y,z))+Δrobot(i)  (4)

[0061] Where f(x,y,z) is the ideal model of the workpiece, usually theCAD model and Δrobot(i) is the error from the robot.

[0062] Thus the relative error will become:

Relative Error(i)=Δwork-object frame(i)+ε  (5)

[0063] Where ε is the random error from robot repeatability.

[0064] According to this principle, setting up the relative referenceand measuring the relative error will be two major tasks in relativecalibration. The detailed procedure of setting up the relative referenceis as follows. First make a sample working-object as identical to CADmodel as possible. Second, generate the calibration path on the surfaceof the sample-working object, simulating the path of robot operation inthe simulation environment. Third, contact the robot 12 with thecalibration sensor 52/54 and set to zero. In this way, a closed-formkinematic chain is formed. Fourth, move the robot 12 along thecalibration path to measure the relative error using the calibrationstation 50. Fifth, add this error into the path generated from the CADmodel to form a relative zero reference for the entire path.

[0065] The next step in the calibration process is relative errormeasurement. The sample working-object is removed and a realworking-object or workpiece is installed in gripper 30. The robot 12moves the real working object toward the calibration sensor 52/54 of thecalibrations station 50. The sensor is set to zero when the workingobject surface touches the sensor 52/54.

[0066] The measurement is designed to decouple the error matrix into twoparts as (Δx, Δy, Δθ) and (Δz, Δa, ΔD), where (Δx, Δy, Δθ) are theoffset of work-object coordinate from the mounting plate 14 in the X-Ydirection and Δθ is the orientation error around the Z-axis. In thesecond group (Δz, Δα, Δβ), Δz is the distance variation along theZ-direction and Δa, Δβ are the orientation angle errors along thedirection of pitch and yaw (see FIGS. 8 and 9).

[0067] The (Δx, Δy, Δθ) can be obtained by measuring the closedtwo-dimensional sectional workpiece profile. In order to get (Δz, Δα,Δβ), multiple sections of the closed two-dimensional profile ofmeasurements are needed and the displacement of the workpiece along theZ-axis needs to be measured too.

[0068] In the example described herein, it should be ensured that atleast three sections on the surface along the z-direction are measuredand one distance in z-direction is measured to get a complete data setfor 6 degrees of freedom (DOF) information. It is important to recordthe data in a steady state in order to get stable and repeatable data.

[0069] The detail procedure is as follows. First, define the stand offpoints, which set up the relative zero when the kinematic chain isclosed. This is also known as the relative zero point. Second, definethe calibration path (i.e. define via points to go to from the stand offpoints). The calibration path will be designed to not only cover all 6degrees of freedom (DOF) errors collection, but also to decouple (Δx,Δy, Δθ) and (Δz, Δα, Δβ). Third, move the workpiece to a first standoffpoint and set up zero. Fourth, move to the calibration points along thedesigned paths. Fifth, record the true relative displacement from thecalibration sensor 52/54. Finally, obtain the errors for all calibrationpoints.

[0070] The fourth step is the calibration parameters (i.e. virtualwork-object frame error-matrix) calculation. The calculation essentiallybecomes a two-stage non-linear optimization problem as shown in FIG. 9.

[0071] The first stage is to minimize the distance error between thetrue value and relative reference in one section of closed profile. Thenon-linear optimization problem consists of finding a set of (Δx, Δy,Δθ) to minimize:

D(i)=Minimize[(X(i)−f _(x)((Δx, Δy, Δθ)]²+[(Y(i)−f _(y)((Δx, Δy, Δθ)]²+[Z(ι)−f _(z)((Δx, Δy, Δθ)]².)  (6)

[0072] Where (X(i), Y(i), Z(i)) are the coordinates for an ideal target,f_(x), f_(y), f_(z) are the components of the true coordinate of f((Δx,Δy, Δθ) and D(i) is the relative distance function.

[0073] As soon as optimal value (Δxmin, Δymin, Δθ_(min)) are obtained,the second optimization step is to find a set of (Δz, Δa, Δβ) tominimize: $\begin{matrix}{\quad \begin{matrix}{{{Sum}\quad {of}\quad \left( {D(i)} \right)} = {{Minimize}\left\lbrack \left( {{x(i)} - {f_{x}\left( \left( {{\Delta \quad x\quad \min},{\Delta \quad y\quad \min},{\Delta \quad \theta \quad \min},{\Delta \quad z},{\Delta\alpha},{\Delta \quad \beta}} \right) \right\rbrack}^{2} +} \right. \right.}} \\{\left\lbrack \left( {{Y(i)} - {f_{y}\left( \left( {{\Delta \quad x\quad \min},{\Delta \quad y\quad \min},{\Delta \quad \theta \quad \min},{\Delta \quad z},{\Delta\alpha},{\Delta \quad \beta}} \right) \right\rbrack}^{2} +} \right. \right.} \\{\left\lbrack {{Z(\iota)} - {f_{z}\left( \left( {{\Delta \quad x\quad \min},{\Delta \quad y\quad \min},{\Delta \quad \theta \quad \min},{\Delta \quad z},{\Delta\alpha},{\Delta \quad \beta}} \right) \right\rbrack}^{2}} \right)}\end{matrix}} & (7)\end{matrix}$

[0074] Iteratively repeat these two stages until all of the sectionerrors are minimized as shown in FIG. 10b. By using each section data,Δx, Δy, Δθ will be obtained for each path. Next use the multiplesections data to to get (Δx, Δy, Δθ, Δα, Δβ). Then apply updated (Δx,Δy, Δθ, Δα, Δβ) to the simulation to get simulated offset for eachtargets along the paths. Next deduct offset from current offset to getthe new offset, repeat the above algorithm to get a new (Δx, Δy, Δθ, Δα,Δβ). If new the (Δx, Δy, Δθ, Δα, Δβ) in step 4 is small enough, get outof the loop, otherwise, add the new (Δx, Δy, Δθ, Δα, Δβ) to the current(Δx, Δy, Δθ, Δα, Δβ), then repeat the above three steps. In this way,(Δx, Δy, Δθ, Δα, Δβ) will be obtained and the virtual work-objectcoordinate frame error matrix will be formed.

[0075] The final step is relative tool frame calibration. In theprevious steps, the tooling system has not been involved because thecalibration station 50 simulates the role of tooling system 40.Therefore it is now necessary to perform relative calibration betweenthe tool 42 and the sensor 52/54 of the calibration device.

[0076] The steps in the tooling calibration are shown in the flowchartof FIG. 11. First, move the robot 12 to contact a point between therobot 12 and the tooling system 40. Run though the operation path torecord the force utilizing force sensor 20 at each contact point andconstruct a stiff matrix for the force in 6 DOF. Based on the stiffmatrix, which describes the relationship between the force and theincremental displacement of (Δx, Δy, Δz), the displacement error matrixwill be obtained. Convert this error matrix to normal and tangentialdecomposition respectively. The position and orientation of the toolwill be obtained. The calibrated error will be compensated for thetooling coordinate system fixed TCP.

[0077] In the case that there is not an on-line force sensor 20 in theworkcell, there is another way to accomplish tooling calibration. Therobot 12 holds a linear gauge 52/54 to calibrate the orientation of thefixed tool center point, for example on the contact wheel 46 of thetooling system 40. By simply measuring the relative difference betweenany two points on the contact wheel, the orientation of the tool centerpoint on the contact wheel can be calculated.

[0078] The above five steps will complete all of the workcellcalibration and they are completed entirely off line.

[0079] Since the TCP calibration and tooling system calibration onlyneeds to be completed once, the reference set up also only needs to becalibrated once for one type of application. Therefore, the on-linecalibration requires only two steps. The two steps include onlinerelative error measurement and calibration matrix calculation. Both ofthese steps can be performed in real-time, which is another advantage ofthis invention.

[0080] The detailed steps for online calibration are as follows. Therobot 12, gripping a real workpiece 32, approaches the calibrationstation 50 to perform the on-line calibration. The gauge 52/54 is set tozero when the robot 12 moves to a first target on the workpiece 32. Theoffset between the programmed path and the real path is recorded at eachof the corresponding target points on the workpiece 32. Graphically,this produces an output like that shown in FIG. 10a for a blade-typeworkpiece 32. The difference in the work-object coordinate system (i.e.gripper 30) between the real workcell and the CAD model is calculated bythe recorded data. Finally, the calibration matrix for the work-objectframe will be added into the work-object coordinate frame or virtualTCP.

What is claimed is:
 1. In a robotic workcell having a robot, a sampleworkpiece, a calibration station and a tooling system, a method foroff-line relative calibration comprising the steps of: determining thetool center point of the robot; creating a relative reference betweenthe robot and the sample workpiece; making relative measurements of thesample workpiece to calculate calibration parameters; calculating awork-object coordinate compensation matrix; and calibrating the toolingsystem.
 2. In a calibrated robotic workcell having a robot, a trueworkpiece, a calibration station and a tooling system, a method foron-line relative calibration comprising the steps of: making relativemeasurements of the true workpiece to calculate calibration parameters;and calculating a work-object coordinate compensation matrix.
 3. In arobotic workcell having a robot, a sample workpiece, a true workpiece, acalibration station and a tooling system, a method for calibrationcomprising the steps of: determining the tool center point of the robot;creating a relative reference between the robot and the sampleworkpiece; making relative measurements of the sample workpiece tocalculate calibration parameters; calculating a work-object coordinatecompensation matrix; calibrating the tooling system; making relativemeasurements of the true workpiece to calculate calibration parameters;and re-calculating the work-object coordinate compensation matrix. 4.The method of claim 1 wherein determining the tool center pointcomprises the steps of: selecting a calibration target having knowngeometric parameters; touching the target from random direction, atleast two different directions to measure the variation from the knowngeometric parameters; and calculating the tool center point.
 5. Themethod of claim 4 wherein the tool center point is calculated bynon-linear least square optimization.
 6. The method of claim 1 whereincreating the relative reference between the robot and the sampleworkpiece comprises the steps of: grasping the sample workpiece;measuring the sample workpiece in a plurality of locations; andcalculating the difference between a perfect model of the workpiece andthe sample workpiece and adding all measured errors to the perfect modelto construct a relative reference.
 7. The method of claim 1 whereingenerating the relative error map comprises the steps of: measuring atwo dimensional cross-section closed profile of the workpiece todetermine errors in a X-Y plane for (Δx, Δy, Δθ), where Δθ representsthe direction of roll; measuring multiple two-dimensional cross-sectionclosed profiles of the workpiece along a Z direction to determine errorsin a Y-Z plane for (Δz, Δα, Δβ), where (Δα, Δβ) represent the directionof yaw and pitch.
 8. The method of claim 1 wherein calculating awork-object coordinate compensation matrix comprises the steps of:optimizing an offset and orientation along the workpiece in a firstplane; optimizing an offset and orientation along the workpiece in asecond plane; iteratively repeating the first and second steps until allrelative errors are minimized.
 9. The method of claim 1 whereincalibrating the tooling system comprises the steps of: moving the robotto a first contact point between the robot and the tooling system;recording the force between the robot and tooling system; repeating theabove procedure until only a substantially normal force is generated;transferring and calculating the residual error between the robot andthe tooling system by converting force error components into positionvariation; and calculating the error-compensation matrix and adding intoa tooling coordinate frame.
 10. The method of claim 1 whereincalibrating the tooling system comprises the steps of: measuring therelative difference between the fixed tool center point on the toolingsystem and the calibration station.
 11. The method of claim 1 whereincalibrating the tooling system comprises the steps of: touching therobot to the tooling at a first location and recording the robotposition; touching the robot to the tooling at a second location andrecording the robot position; calculating the relative differencebetween the robot TCP and a parameter defined by the first and secondlocations.
 12. In a robotic workcell having a robot, a roboticcontroller, a sample workpiece, a true workpiece, a sensor and a toolingsystem, a method for relative calibration comprising the steps of:downloading a model of the workpiece into the robotic controller;determining the tool center point of the robot; creating a relativereference between the robot and the sample workpiece; making relativemeasurements of the true workpiece to calculate calibration parameters;calculating a work-object coordinate compensation matrix; andcalibrating the tooling system.
 13. In a robotic workcell having arobot, a sample workpiece, a calibration station and a tooling system, amethod for calibration comprising the steps of: calibrating the robotutilizing the sample workpiece and a digital model of the workpiece;taking relative measurements of the sample workpiece to calculatecalibration parameters; and calculating a work-object coordinatecompensation matrix.
 14. In a robotic workcell having a robot, a sampleworkpiece, a true workpiece, a calibration station and a tooling system,a method for calibration comprising the steps of: calibrating the robotutilizing the sample workpiece and a digital model of the workpiece;taking relative measurements of the sample workpiece to calculatecalibration parameters; calculating a work-object coordinatecompensation matrix; making relative measurements of the true workpieceto calculate calibration parameters; and re-calculating the work-objectcoordinate compensation matrix.
 15. A relative calibration system foruse in a robotic workcell including a computer controlled robot, thesystem comprising: a calibration target mounted within the workcell; atrue workpiece located within the workcell; and a sensor located withinthe workcell whereby the computer controlled robot determines a toolcenter point of the robot and establishes a relative reference betweenthe workcell and the true workpiece.
 16. The system of claim 15 whereinthe sensor is a linear gauge.
 17. The system of claim 15 wherein thesensor is a non-contacting gauge.
 18. The system of claim 15 wherein thecalibration sample is a sphere.
 19. The system of claim 15 wherein thecalibration sample is a cylinder.
 20. The system of claim 15 wherein thecalibration sample is a cubic.
 21. The system of claim 15 wherein thecalibration sample is a geometric shape.
 22. A tooling calibrationsystem for use in a robotic workcell including a computer controlledrobot, the system comprising: a force sensor mounted to the robot; adata collection device connected to the force sensor; a workpieceremovably connected to the force sensor; and a tool mounted within theworkcell whereby the force between the workpiece and robot is measuredby the force sensor, collected by the data collection device andmathematically optimized to calibrate the tool position.
 23. A toolingcalibration system for use in a robotic workcell including a computercontrolled robot, the system comprising: a sensor removably attached tothe robot; a data collection device connected to the sensor; and a toolmounted within the workcell whereby the relative position of at leasttwo points are recorded by the data collection device and the toolposition is determined.